Linear Transformations

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What effect does replacing f(x) with 2f(x) have on the graph of f(x)?

Back

It results in a vertical stretch of the graph by a factor of 2.

Front

What does a vertical translation of a graph mean?

Back

A vertical translation moves the graph up or down without changing its shape.

Front

What is the effect of a horizontal translation on a graph?

Back

A horizontal translation shifts the graph left or right without changing its shape.

Front

What does it mean for a graph to be reflected?

Back

A reflection flips the graph over a specified axis, such as the x-axis or y-axis.

Front

How does a vertical compression affect a graph?

Back

A vertical compression reduces the height of the graph, making it flatter.

Front

What is the result of applying a factor of 1/3 to a function f(x)?

Back

The graph of the function becomes less steep, resulting in a vertical compression by a factor of 1/3.

Front

What does it mean for a graph to be steeper?

Back

A steeper graph has a greater slope, indicating a faster rate of change.

Front

How can you describe the transformation from f(x) to g(x) if g(x) is a vertical translation of f(x)?

Back

The graph of g(x) is shifted up or down by a certain number of units compared to f(x).

Front

What is the effect of a vertical stretch by a factor of k on a function f(x)?

Back

The graph of f(x) is stretched away from the x-axis by a factor of k, making it taller.